Finding inital velocity

A ball is kicked horizontally off a cliff 40m high. After 3seconds, the person that is on top of the cliff hears the thump of the ball hitting the floor. Assuming speed of sound travles 343m/s in air, what is the initial velocity that the ball was kicked at?

Please check if I did it correct....

Find time it takes for the ball to hit the floor:
d=.5at^2
40m=.5(9.8)(t^2)
t=2.857142857 s

Find time it takes for the sound to travel back to person on cliff:
3-2.857142857=.1428571429

Find the distance away from cliff:
d=vt
d=343*.1428571429
d=49

Find the distance travled in the x-direction:
49^2=40^2+x^2
x=28.3019434m

Since the ball was kicked at an initial velocity [tex]v_1[/tex], [tex] d = v_1t + \frac {1}{2}at^2[/tex]
You're solving for [tex]v_1[/tex] eventually. The calculation you made for v after that was the average velocity which isn't entirely right.

Since the ball was kicked at an initial velocity [tex]v_1[/tex], [tex] d = v_1t + \frac {1}{2}at^2[/tex]
You're solving for [tex]v_1[/tex] eventually. The calculation you made for v after that was the average velocity which isn't entirely right.

I was solving for the time it took the ball to drop. It has no initial velocity.

vsage said:

The easiest thing to do in the question is solve for how much time it takes for the sound to travel back up. since t = d/v you know how much time it took for the sound to move 40m. The total time for the events in the question to occur was 3 seconds. How much time did the ball spend falling then? You now have only one unknown in the kinematics equation I gave above. I hope this helps.

Staff: Mentor

UrbanXrisis said:

A ball is kicked horizontally off a cliff 40m high. After 3seconds, the person that is on top of the cliff hears the thump of the ball hitting the floor. Assuming speed of sound travles 343m/s in air, what is the initial velocity that the ball was kicked at?